A subset of the ground set is called independent if it is contained in a basis, or equivalently, does not contain a circuit. This method returns all independent subsets of the ground set of a fixed size $s$. If no size $s$ is given, returns a list of all independent sets of M.
i1 : M = matroid({a,b,c,d},{{a,b},{a,c}})
o1 = a matroid of rank 2 on 4 elements
o1 : Matroid
|
i2 : independentSets(M, 2)
o2 = {set {0, 1}, set {0, 2}}
o2 : List
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i3 : netList independentSets M
+----------+
o3 = |set {} |
+----------+
|set {0} |
+----------+
|set {1} |
+----------+
|set {0, 1}|
+----------+
|set {2} |
+----------+
|set {0, 2}|
+----------+
|
i4 : V = specificMatroid "vamos" o4 = a matroid of rank 4 on 8 elements o4 : Matroid |
i5 : I3 = independentSets(V, 3)
o5 = {set {0, 1, 2}, set {0, 1, 4}, set {0, 2, 4}, set {1, 2, 4}, set {0, 1,
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3}, set {0, 3, 4}, set {1, 3, 4}, set {0, 2, 3}, set {2, 3, 4}, set {1,
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2, 3}, set {0, 1, 5}, set {0, 2, 5}, set {1, 2, 5}, set {0, 3, 5}, set
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{1, 3, 5}, set {2, 3, 5}, set {0, 4, 5}, set {1, 4, 5}, set {2, 4, 5},
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set {3, 4, 5}, set {0, 1, 6}, set {0, 2, 6}, set {1, 2, 6}, set {0, 3,
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6}, set {1, 3, 6}, set {2, 3, 6}, set {0, 4, 6}, set {1, 4, 6}, set {2,
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4, 6}, set {3, 4, 6}, set {0, 5, 6}, set {1, 5, 6}, set {2, 5, 6}, set
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{3, 5, 6}, set {4, 5, 6}, set {0, 1, 7}, set {0, 2, 7}, set {1, 2, 7},
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set {0, 3, 7}, set {1, 3, 7}, set {2, 3, 7}, set {0, 4, 7}, set {1, 4,
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7}, set {2, 4, 7}, set {3, 4, 7}, set {0, 5, 7}, set {1, 5, 7}, set {2,
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5, 7}, set {3, 5, 7}, set {4, 5, 7}, set {0, 6, 7}, set {1, 6, 7}, set
------------------------------------------------------------------------
{2, 6, 7}, set {3, 6, 7}, set {4, 6, 7}, set {5, 6, 7}}
o5 : List
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i6 : #I3 o6 = 56 |